Buiding Services Compass Survey
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Definitions
Defect or Error
• Stress in member exceeds limiting value permanently
Failure
• Failure means the structure may collapse or totally
fails to perform the designed function
Decay:
• Development of defect due to aging
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Repair:
• Technical aspect of rehabilitation
Rehabilitation:
• Restoring structure to service level
Damage:
• Sequence of defects
Distress:
• Visible or Hidden signs of damage
Contd…
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Causes of Failure
• Inadequate maintenance
• Bad use of building
• Poor workmanship in construction
• Defective construction materials
• Defective construction practices
• Wear and tear
• Weathering
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• Regular maintenance
• Stopping leakage in:
– Roof
– Walls
– Soil pipes
– Plumbing
– Waste water pipes
– Rain water pipes
Remedies to arrest Decay ( Failures )
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Use of:
1. Specified materials
2. Good workmanship during construction
3. Protection against weathering agencies
4. Protection against aggressive environment
5. Avoid overloading
Contd…
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Classification of Failures
Failures can be broadly classified
• Structural failures
• Non structural failures
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Structural Failures
Causes :-
These are due to
1. Incorrect design
2. Faulty construction
3. Over loading
Example : Extensive cracking of the RCC beam.
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Non-structural failures
• These are due to
– Internally induced stresses in building materials
– Penetration of moisture
– Weathering action
Causes :-
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• The non- structural cracks are not a threat to the safety
of building. But they – Look ugly
– Creates impression faulty work
– May give a feeling of instability
Example:
• Vertical cracks in a long compound wall due to – Shrinkage
– Thermal movement .
Contd…
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Failures in Concrete
• Concrete being most widely used, we deal with failures
in concrete. They are
– Cracking
– Spalling
– Disintegration
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Classif ication of Cracks (Based on Width of
Crack )
• Fine: less than 0.5 mm
• Thin : 0.1 mm to 0.3 mm
• Wide: 0.7 to 2.0 mm
• Very wide: 0.7 to 2.0 mm
C td
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Photo1. Vertical Cracks in RCC Railing due to drying shrinkage
of concrete and thermal movement
Contd…
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Photo 2. Vertical crack at the junction of two blocks of residential
flats, each block being about 20m in length
Contd…
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Fig.1.Temperature cracking in Building
Contd…
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Photo.3 Photo.4
Contd…
Contd
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Photo.5 Photo.6
Contd…
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Effects of Over Loading
• Excessive cracking due to :
• Flexure
• Shear
• Diagonal tension
• Compression
• Shear bond failure
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• Column surface spalling due to:
• Excessive compressive stress
• Large deflection
• Cracking in slabs
• Settlement of foundation
Contd…
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Types of Structural Cracks
Due to
• Pure flexure
• Pure tension
• Shear
• Torsion
• Bond
• Concentrated load
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Common forms of failure
• Corrosion of reinforcement
• Alkali and sulphate attack
• Displacement of the system
• Excessive deformation
• Malfunctioning of expansion joints
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Effects of Failures
• Plastic Deformation
• Shrinkage Cracks
• Contraction Cracks
• Cracks Due To Reinforcement Corrosion
• Alkali Aggregate Reaction
• Frost And Sulphate Attack Cracking
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Fig.2 Environment soil structure interaction and resultant
pattern of cracking
Contd…
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Defects in Masonry Structures
• Dampness
• Condensation
• Efflorescence
• Structural cracks
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Strengthening with
• Mild steel plates
• Jacketing techniques
• Fiber reinforced concrete
• Shotcrete
• Ferrocement
• Steel reinforcement and grouting
Strengthening of Members Failed Under
Torsion
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Procedure For Applying FRP SheetsPhoto 7
Contd…
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Procedure For Applying FRP SheetsPhoto 8
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Photo.9 Procedure For Applying FRP Sheets
Contd…
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Photo.10 Procedure For Applying FRP Sheets
Contd…
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Photo.11 Procedure For Applying FRP Sheets
Contd…
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Photo.12 Procedure For Applying FRP Sheets
Contd…
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Photo.4
Photo.13 Procedure For Applying FRP Sheets
Contd…
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Photo.14 Procedure For Applying FRP Sheets
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Photo.15 Procedure For Applying FRP Sheets
Contd…
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Glass Fibre
Carbon Fibre
Retrofitting
Technique
Photo.17
Photo.18
Contd…
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Strengthening of column using concrete jacketing
Fig.3
Contd…
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Strengthening of column using steel jacketing Photo.19
Contd…
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Strengthening of column using CFRP wrap Photos.20 and 21
Contd…
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Strengthening of beam using steel jacketing Fig.4
Contd…
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• Application of bonding agent over the old surface
• Covering with welded mesh
• Preparation of mortar
• Plastering
• Curing
Procedure For Applying Ferrocement
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• Preparation of form work to cover all sides of beam
• Application of bonding agent
• Preparation of micro concrete
• Filling form work with micro concrete and finishing
• Curing
Procedure For Applying Microconcrete
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• Trees should not be grown in expansive soils and clay
adjacent to buildings
• Trees like ashoka and coconut do not cause distress and
harm less
• Roots of trees like jack fruit spread horizontally: harmful tostructures
Precautions To Prevent Cracks Due To
Vegetation
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Failures of Foundations
Main causes of failure of foundations
1. Unequal settlement of the sub soil.
2. Unequal settlement of the masonry.
3. Withdrawal of moisture from the sub soil
4. Lateral pressure on the superstructure
5. Horizontal movement of the earth
6. Transpiration of trees and shrubs
7. Atmospheric action
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Construction Failures Repairs Maintenance
And Building Services
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Non-structural Failures
Failure of Masonry Structures
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Principal causes of cracks
a) Moisture changes,
b) Thermal variations,
c) Elastic deformation,
d) Creep,
e) Chemical reaction,
f) Foundation movement, and settlement of soil, and
g) Vegetation.
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Defects in Masonry Structures
• Dampness
• Condensation
• Efflorescence
• Structural cracks
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• Surface cracks
• Stains
• Defects in plastering
• Defects in repair work
Contd…
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• Cracks due to tensile stresses
• Flexural tension at lintel level
• Shear cracks
Cracks in Masonry Walls
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Tensile crack in a masonry wallFig.1
Contd…
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Flexural Tension Crack in Wall MasonryFig.2
Contd…
Contd…
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Shear crack in Masonry wallFig.3
Contd…
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Shear crack in masonry pillar due to
expansion of RCC beam
Fig.4
Contd…
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Cracking Due to Expansion of BrickworkFig.5
Contd…
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Cracking in Top most storey of a Load Bearing Structure
Fig.6
Contd…
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Cracking due to expansion of brickworkFig.7
Contd…
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RCC Roof Slab Over Masonry WallFig.8
Contd…
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Cracking in Cladding and Cross Walls qf a FramedStructure
Fig.9
Contd…
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Fig.10 Arching up and Cracking of Coping Stones of a
Long Garden Wall
Contd…
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Fig.11 Horizontal Crack at the Base of Brick Masonry
Parapet
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• Shear cracks in masonry pillar at beam support
• Cracks due to expansion of brick work
• Cracks in topmost storey of load bearing structure
Cracks in Masonry Walls
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• Diagonal cracks in cross walls of multi storeyed load
bearing structure
• Vertical cracks at window openings
• Horizontal cracks in wall at supports
• Cracking of compound wall due to roots
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• Cracks in walls due to trees close to buildings
• Horizontal cracks in top most storey due to
shrinkage and deflection of slab
• Diagonal cracks at corners of building due to
foundation settlement
Contd…
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Diagonal cracks in cross walls of multi-storied load bearing
structures
Fig.12
Contd…
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Fig. 13 Vertical Cracks in multi-storied buildings having
window openings in load bearing wall
Contd…
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Fig. 14 Horizontal cracks in a wall at supports due to
excessive deflection of a slab of large span
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Cracking of a compound wall due to growing roots under the
foundation
Fig.15
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Trees growing close to a building on shrinkable soil may cause
cracks in the walls
Fig.16
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Fig.17
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Trees Growing Close To A Building On Shrinkable Soil May
Cause Cracks In Walls
Fig.18
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Horizontal cracks in top-most storey below slab due to
shrinkage and deflection of slab
Fig.19
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Horizontal Cracks In Brick Panels Of Framed Structure
Fig.20
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Fig.21 Horizontal Crack at the Base of Brick Masonry
Parapet
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Fig.22 Vertical Cracks at the Junction of RCC Column And
Wall
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Photo.1 Horizontal Crack In Masonry Wall Due To Elastic
Deformation, Shrinkage In Canopy Slab
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Photo.2 Horizontal cracks in compound wall of brickwork,
having horizontal reinforcement
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Photo 3 Diagonal crack in the corner of a building due to
foundation settlement
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Fig.23 Horizontal Cracks In Brick Panels Of Framed
Structure
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Fig. 24 Vertical Crack In Brick Panel Wall Due ToExpansion Of Brick Work
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Fig. 25 Vertical crack in brick panel wall of framed structure
due to expansion of brick work
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Fig.26
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Fig.27
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Fig.28
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Fig.29
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Fig.30
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Fig.31
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Fig.32
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Photo 4
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Fig.33
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Fig.34
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PHOTO 5
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Fig.35
Cracks in Masonry Walls
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Remedy:
• Strengthening of foundation
• By underpinning
• Grouting
• Strengthening of members
• Ferrocement for repair and rehabilitation
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• Do not directly affect the structural safety
• Penetration of moisture through cracks:
• Leads to structural failure
• Spoiling of internal finish
Non - Structural Failures
Causes of Non - Structural Cracks
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• Moisture changes
• Thermal variations
• Creep
• Chemical reactions
• Settlement of soil
• Vegetation
• Shrinkage at the time of initial drying
• Absence of expansion/contraction joints
Precautions / Remedies to Prevent Non-
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• Proper grading of concrete
• Compaction by vibrator
• Maintenance of water cement ratio
• Proper curing
• Cleaning of aggregates
• Avoid bleeding of concrete
• Covering concrete with wet canvas
Precautions / Remedies to Prevent Non
structural Cracks
Contd…
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• Plastering masonry –after drying of curing
Drying for about 3 months
• Providing shrinkage reinforcement
• 0.25% of cross sectional area of concrete
– use small bars at closer intervals
• Plastering of concrete structures immediately afterremoval of shuttering
• Provide strip joints between slab and supporting wall inload bearing structures
Contd…
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• Adequate insulation to roof slabs
• Expansion joints in long walls @ 15 m intervals
• Masonry construction over RCC slabs – 15 days
after removal of form work
Contd…
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• In RCC framed structure:
• completion of frame work before construction of
masonry walls
• Construction of partition walls commences from top
Contd…
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• In masonry partitions having length to height ratio >
2: provide horizontal reinforcement
• If soluble sulphates present in soil, ground water, or
clay bricks: use rich mix and sulphate resistant
cement
• Do not use bricks containing more than 1% soluble
sulphates
Contd…
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• Provide under reamed pile foundation in expansive
soils
• Provide adequate cover to reinforcement
• Horizontal extension of building separated from the
old by expansion joint right from bottom to top
• No excavation below the foundations of old buildings
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Precautions to Prevent Cracks due to
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• Trees should not be grown in expansive soils and
clay adjacent to buildings
• Trees like ashoka and coconut do not cause distress
• Roots of trees like jack fruit spread horizontally:
harmful to structures
Vegetation
Cracks In Masonry
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Causes:
• Poor quality of materials
• Bad workmanship
• Uneven settlement of foundation
• Heavy concentration of loads
• Impact loads
• Vibrations
• Improperly designed lintels and beams
Repairs to Cracks in Masonry
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Cement grouting to minor cracks:
• Clean cracked surface
• Wash with water
• Fill crack with cement grout by cement gun
p y
Contd…
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• Repair to wider cracks using expanding cement slurry
• Clean cracked surface
• Wash with water
• Fill crack with expanding cement grout by cement gun
• Cement expands after setting
Failure in plastering
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p g
1. Blistering of plastered surface
2. Cracks
3. Efflorescence
4. Flaking
5. Peeling
6. Popping
7. Rust-stains
8. Softness
9. Uneven surface
Remedies
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1. Plastering should be carried out in the last
workmanship manner.
2. Bond of brick work should be properly maintained.
3. Efflorescence is removed by rubbing brushes on the
damaged surface. A solution of (one part of Hcl or H2
SO4 + five parts of clean water)
4. Bricks of superior nature be used
5 W t f f lt b d f b i k k d
Contd…
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5. Water free from salts be used for brick work and
plastering work.
6. Surface to be plastered be well-watered
7. Excessive trowelling be avoided.
8. Damp- proof courses be provided at convenient place
in the building.
Leakage of R.C.C Roofs
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Causes:
• Harsh and poorly designed mix
• Poor compaction
• Excess water cement ratio
• Excess fine aggregate
• Use of fine sand
Contd
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• Improper curing
• Thermal expansion
• Failure of expansion joints
• Improper removal of farm work
Contd…
Prevention is better than cure. Therefore water proofing of
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roof is made by employing any one of the following
methods:
• Finishing of roof surface is done at the time of laying
cement concrete. The C.M proportion is 1:4
• Bedding concrete and flooring
• Application of Mastic asphalt and jute cloth
But despite the fact that all the care is taken still leakage
may occur
Prevention of Leakage in R.C.C Roofs
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• Using well designed mix
• Application of:-
– Membrane water proofing
– Cement base paints
– water repelling agents
Contd…
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• Application of surface coat with mixture of ordinary
portland cement and any one of :-
– Hydrated lime
– Hygroscopic salts like calcium chloride, sodium
chloride
– Titanium oxide
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Fig.1 Water Proofing of Terrace
Spalling
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Causes:-
1. Corrosion of reinforcements
2. Sudden changes in temperature
3. Thermal expansion
4. Improper cover
5. Segregation
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Photo.1 Underside of slab deterioration due to water leakage
through slab crack
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Photo 2 Concrete deterioration due to water leakage through
slab crack
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Repair of Spalling
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1. Defective area should be scarified
2. Cleaned of all loose materials
3. Surface kept moist for fourteen hours
4. Strengthening by mat reinforcement
5. Guniting dense concrete
6. Curing
Repair of Spalling
Failures in Flooring
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g
• The common types of failures in flooring• Pitting
• Cracking
• Spalling at joint
• The reasons are
• Wear and tear
• Accident
Pitting
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g
• Pitting consists of small holes on the surface due to
– Aggregate becoming loose
– Dents caused by accidents
• The remedial measure is applying
– Epoxy resins with matching colours and cements
Cracking
• This may occur in concrete and terrazzo flooring
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This may occur in concrete and terrazzo flooring
• Reasons are
– Deflection due to load ( upper floors )
– Due to settlement ( ground floor )
• Remedial measures
• In upper floors a cushion layer of lime concrete is
suggested
• In case of ground floor
– Break the flooring totally at the damaged part – Refill properly and relay the floor
• Can also be repaired by expansive grout or by epoxy
Spalling
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p g
• Generally it happens near joints due to weak mortar.
• Remedial measures
• Depth of spall is less than 25mm use epoxy resins.
• The large chunks are found
– Cut the spalling area in a regular way
– Reconcrete with a binder like araldite , epoxy etc.,
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COMPASS SURVEYING 125
COMPASS SURVEYING
RAMINENI VENU,
M.TECH(STRUCTURES)
Prepared by:
Purpose and Principle of Compass
C A l i i t t (B i )
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COMPASS SURVEYING 126126
Compass :Angle measuring instrument (Bearing)
Principle: The principle of compass surveying is
traversing
Designation of compass
– The size of the compass is expressed in terms of its
diameter
– The compass 12 cms(120mm) means the diameter of box
is 12 cms(120mm)
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COMPASS SURVEYING 127127
Traversing:
It is a series of connected lines.
Types of traversing:-
(a) Open traverse : continuous lines, not returns
(b) Closed traverse : forms closed circuit
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COMPASS SURVEYING 128128
Fig.1 Sketch of Open Traverse
Contd…
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COMPASS SURVEYING 129129
Fig.2 Sketch of Closed Traverse
Methods of Traversing
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COMPASS SURVEYING 130
g
Chain traversing (by chain angle)
Compass traversing (by free needle)
Theodolite traversing (by fast needle)
Plane table surveying (by plane needle)
When is Compass surveying recommended ?
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COMPASS SURVEYING 131131
Compass Survey is recommended when
A large area is to be surveyed
The course of a river or coast line is to be surveyed
The area is crowded with many details and triangulation is not
possible
p y g
When is Compass surveying not recommended ?
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COMPASS SURVEYING 132
•Where local attraction is suspected due to magnetic material
steel , iron & electric cables
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COMPASS SURVEYING 133
Types of compass
There are two types of Compass
1. Prismatic Compass(0 to 360 Degrees)
2. Surveyor’s Compass(0 to 90 Degrees)
Prismatic Compass
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COMPASS SURVEYING 134
Fig.3 Sketch of Prismatic Compass
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COMPASS SURVEYING 135135
Fig.4
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COMPASS SURVEYING 136
Parts of Prismatic Compass
Compass Box:
– Circular 8 to 10 cm (80mm to 100mm) metallic
– At the center of box pivot is provided.
Magnetic Needle and Graduated Ring: – On pivot the magnetic needle rests
– Aluminium graduated ring is attached to needle
– Graduated ring has 0 degree to 360 degrees clockwise
– i.e. 00 at south ,900 at west ,1800at north ,2700 at east
– Least count is 30minutes
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Contd…
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COMPASS SURVEYING 138
Sight vane and Object vane Of Compass:
– Sight vane and Object vane are fixed diametrically opposite tothe each other.
– Object vane consists of vertical hair attached to the frame
– Sight vane ( or eye slit )consists of vertical slit cut into upperassembly of the prism unit
– Prism unit is hinged to the box
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COMPASS SURVEYING 139
Dark Glasses
–Red glasses Sighting luminous objects.
–Blue glasses Reduces strain to observer.
Adjustable Mirror
Contd…
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COMPASS SURVEYING 140
j
– Provided with sight vane horizontally vertically and Inclined
manner .
Brake Pin
– At the base of sight vane. If pressed, oscillation is stopped
Lifting Pin
– Below the sight vane
– Lifts magnetic needle
Adjustments of Prismatic Compass
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COMPASS SURVEYING 141
j p
Fixing the compass with tripod stand.
Centering.
Leveling.
Adjustment of prism.
Observation of bearing.
Definitions:-
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Bearing of the line:- The horizontal angle made by the
survey line with some fixed reference direction is bearing of
line.
The fixed reference is known as Meridian
The meridians are
– True meridian
– Magnetic meridian
– Arbitrary meridian
True Meridian: It is the line passing through the pointand joining the North and South poles of the earth
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COMPASS SURVEYING 143
and joining the North and South poles of the earth.
Q
P
A
Line PAQ is the True Meridian
Fig.3
True Bearing: It is he horizontal angle made by the surveyline with the true meridian
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COMPASS SURVEYING 144
Fig.4
Magnetic Meridian: The direction shown by a freely
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suspended well balanced Magnetic Needle at any point is
termed as Magnetic Meridian
Fig.5
Magnetic Bearing: Horizontal angle made by the surveyline with the magnetic meridian.
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COMPASS SURVEYING 146
Fig.6
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COMPASS SURVEYING 147
Arbitrary Meridian: Any arbitrarily assumed directionchosen to measure the bearings is termed as Arbitrary Meridian
Arbitrary Bearing: The horizontal angle made by the
survey line with the arbitrary meridian
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COMPASS SURVEYING 148
Bearings are designated by two systems
– Whole Circle Bearing ( WCB )
– Quadrantal Bearing or reduced bearings( QB or RB )
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COMPASS SURVEYING 149
Whole circle bearing (W.C.B.) :
The bearing of a line measured from the North in clockwise
direction.
The value of WCB varies from 00 to 3600
Sketch Of Whole Circle Bearing (W.C.B.)
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COMPASS SURVEYING 150
O
D
C
A
B
WCB of OA = Ө1
WCB of OB = Ө2
WCB of OC = Ө3
WCB of OD = Ө4
Fig.1
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COMPASS SURVEYING 151
Quadrantal Bearing Or Reduced Bearing (Q.B. or R.B.)
The bearing of a Line observed either from the North or South
Measured in Clockwise (or) Anticlockwise direction
Towards East or West
The value of QB ranges between 0
0
to 90
0
Sketch of Reduced (Quadrantal) Bearing
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COMPASS SURVEYING 152
R.B of OA = N θ10 E
R.B of OB = S θ20 E
R.B of OC = S θ30 E
R.B of OD = N θ40 E
o
D
C
A
B
Rules For Conversion Of Bearing FromW.C.B. To Q.B. (R.B.)
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COMPASS SURVEYING 153
Table.1
Line lying in
The quadrant
W.C.B lying between Rule for conversion
to Q.B.
Quadrant
I. 00 to 900 R.B. is same as
W.C.B.
N.E.
II. 900 to 1800 RB = 1800 – WCB S.E.
III. 1800 to 2700 RB = WCB – 1800 S.W.
IV. 2700 to 3600 RB = 3600 – WCB N.W.
Reduced Bearing (Q.B.) To W.C.B.:
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COMPASS SURVEYING 154
Fig.2
Quadrant in
which surveyline lies
W.C.B lying
between R.B.
Rule for conversion to Q.B.
Rule for conversion W.C.B.
Quadrant
W.C.B. lying
between
I. N.E. W.C.B same as R.B. 00 to 900
II. S.E. W.C.B = 180degrees – R.B. 900 to 1800
III. S.W. W.C.B = R.B.+180 degrees 1800 to 2700
IV. N.W. W.C.B = 360 – R.B. 2700 to 3600
Declination: The horizontal angle subtended between the
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COMPASS SURVEYING 155
Declination: The horizontal angle subtended between thetrue meridian and the magnetic meridian.
Declination West Declination East
Fig.7
Contd…
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COMPASS SURVEYING 156
If the Magnetic Meridian is towards East of True
Meridian, the declination is East
If the Magnetic Meridian is towards West of True
Meridian, the declination is West
Fig.8
Contd…
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COMPASS SURVEYING 157
West Declination East Declination
Fig.9
The relation between the true bearing and magnetic bearing of a
line can be written as
Contd…
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COMPASS SURVEYING 158
line can be written as
True Bearing = Magnetic Bearing ± Declination.
For East declination, +ve Sign is to be used where as –ve sign
is used for West declination.
Magnetic Bearing = True Bearing ± Declination
For East declination, –ve sign is to be used where as -ve sign
is used for West declination.
Local Attraction
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COMPASS SURVEYING 159
A magnetic needle indicates the north direction when freely
suspended or pivoted.
Some times the needle comes near some magnetic substances
such as iron ore, steel structures, electric cables conveying
current etc.
Local Attraction
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COMPASS SURVEYING 160
Then it is found to be deflected from its true direction and does
not show the actual magnetic north.
This disturbing influence of magnetic substances is known as
Local Attraction.
Contd…
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COMPASS SURVEYING 161
If all the lines of a traverse are found to be affected by local
attraction
– The line with minimum error is identified
– The fore bearing and back bearing of this line are
adjusted by distributing the error equally
– Then starting from this adjusted line, the fore and back bearings of other lines are corrected
Problems in W.C.B
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COMPASS SURVEYING 162162
1. Convert the following whole circle bearings into quadrantal
bearings.
a) 780201
b) 130030
1
c) 280030
1
d) 232030
1
IIV
N
B
Contd…
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COMPASS SURVEYING 163163
78020l it is in first quadrant
W.C.B = Q.B
78020l = N 78020l E
IIIII
E
S
W A
78020l
IIV
NContd…
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COMPASS SURVEYING 164164
1300
30l
is in second quadrantQ.B = 1800 – W.C.B = SE
Q.B = 1800 - 130030l = S 490301 E
II
III
E
S
W A
B
130030l
IIV
NContd…
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COMPASS SURVEYING 165165
280030l is in fourth quadrant
Q.B = 3600 – W.C.B = 3600 - 280030’
=N 790301 W
IIIII
E
S
W A
B
280030l
IIV
NContd…
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COMPASS SURVEYING 166166
232030l is in third quadrant
Q.B = W.C.B – 1800 = 232030l – 1800
S 52030l W
IIIII
E
S
W A
B
232030l
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COMPASS SURVEYING 167167
2. Convert the following Whole circle bearing into Reduced
bearing.
a) 420151
b) 2230151
c) 3220301
d) 1420301
IIV
N BContd…
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COMPASS SURVEYING 168168
42015l it is in first quadrant
W.C.B = Q.B
Q.B = N 42015l E
IIIII
E
S
W A
42015l
IIV
NContd…
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COMPASS SURVEYING 169169
2230
15l
is in third quadrantQ.B = W.C.B – 1800 = 223015l - 1800
Q.B = S 430151 W
II
III
E
S
W A
B
223015l
IIV
NBContd…
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COMPASS SURVEYING 170170
322030l is in fourth quadrant
Q.B = 3600 – W.C.B = 3600 - 322030l
N 370301 W
IIIII
E
S
W A322030l
IIV
NContd…
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COMPASS SURVEYING 171171
142030l is in second quadrant
Q.B = 1800 – W.C.B = 1800 – 142030l Q.B = S 37030l E
IIIII
E
S
W A
B
142030l
3. Convert the following Whole circle bearing into Reduced
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COMPASS SURVEYING 172172
g g
bearing.
a) 2870
b) 1070451
c) 120
451
d) 1930151
IIV
NContd…
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COMPASS SURVEYING 173173
287000l is in fourth quadrant
Q.B = 3600 – W.C.B
Q.B = 3600 - 287000l
Q.B = N 730 W
IIIII
E
S
W AB
287000l
IIV
NContd…
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COMPASS SURVEYING 174174
107045l is in second quadrant
Q.B = 1800 – W.C.B
Q.B = 1800 – 107045l
Q.B = S 72015l E
IIIII
E
S
W A
B
1070
45l
IIV
NBContd…
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COMPASS SURVEYING 175175
12045l it is in first quadrant
W.C.B = Q.B
Q.B = N 12045l E
IIIII
E
S
W A
12045l
IIV
NContd…
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COMPASS SURVEYING 176176
193015l is in third quadrant
Q.B = W.C.B – 1800
Q.B = 193015l - 1800
Q.B = S 130151 W
II
III
E
S
W A
B
193015l
4 C h f ll i h l i l b i i d d
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COMPASS SURVEYING 177177
4.Convert the following whole circle bearings into reduced
bearings.
a) 500
b) 2300
c) 1450301
d) 325030
1
IIV
N
B
500
Contd…
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COMPASS SURVEYING 178178
500 it is in first quadrant
W.C.B = Q.B
Q.B = N 500 E
IIIII
E
S
W A
500
IIV
NContd…
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COMPASS SURVEYING 179179
2300 is in third quadrant
Q.B = W.C.B – 1800
Q.B = 2300 – 1800
Q.B = S 500 W
IIIII
E
S
W A
B
2300
IIV
NContd…
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COMPASS SURVEYING 180180
145030l is in second quadrant
Q.B = 1800
– W.C.B = SEQ.B = 1800 - 145030l
Q.B = S 340301 E
IIIII
E
S
W A
B
145030l
IIV
NBContd…
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COMPASS SURVEYING 181181
325030l is in fourth quadrant
Q.B = 3600 – W.C.B
Q.B = 3600 - 325030l
Q.B = N 340301 W
IIIII
E
S
W A325
0
30l
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COMPASS SURVEYING 182182
5. Convert the following whole circle bearing into reduced
bearing.
a) 2890271
b) 1090271
c) 2190541
d) 390451
IIV
N
289027l
Contd…
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COMPASS SURVEYING 183183
289027l is in fourth quadrant
Q.B = 3600 – W.C.B
Q.B = 3600 - 289027l
Q.B = N 700331 W
IIIII
E
S
W A
B 289027l
IIV
NContd…
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COMPASS SURVEYING 184184
109027l is in second quadrant
Q.B = 1800 – W.C.B = SE
Q.B = 1800 - 109027l
Q.B = S 700331 E
IIIII
E
S
W A
B
109027l
IIV
NContd…
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COMPASS SURVEYING 185185
2190541 is in third quadrant
Q.B = W.C.B – 1800
Q.B = 2190541 – 1800 Q.B = S 390541 W
IIIII
E
S
W A
B
2190541
IIV
N
BContd…
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COMPASS SURVEYING 186186
390451 it is in first quadrant
W.C.B = Q.B
Q.B = N 390451 E
IIIII
E
S
W A
390451
6 Convert the following whole circle bearing into quadrantal
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COMPASS SURVEYING 187187
6.Convert the following whole circle bearing into quadrantal
bearing.
a) 870531
b) 2670531
c) 780161
d) 2580161
IIV
N
BContd…
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COMPASS SURVEYING 188188
870531 it is in first quadrant
Q.B = W.C.B
Q.B = N 870531 E
IIIII
E
S
W A
870531
IIV
NContd…
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COMPASS SURVEYING 189189
2670531 is in third quadrant
Q.B = W.C.B – 1800
Q.B = 2670531 – 1800 Q.B = S 870531 W
IIIII
E
S
W AB 2670531
IIV
N
B780161
Contd…
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COMPASS SURVEYING 190190
780161 it is in first quadrant
W.C.B = Q.B
Q.B = N 780161 E
IIIII
E
S
W A
B780161
IIV
NContd…
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COMPASS SURVEYING 191191
2580161 is in third quadrant
Q.B = W.C.B – 1800
Q.B = 2580161 – 1800
Q.B = S 780161 W
IIIII
E
S
W A
B
2580161
7. Convert the following W.C.B to Q.B.S
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COMPASS SURVEYING 192192
g Q
a) W.C.B of AB = 45030
1
b) W.C.B of BC = 125045
1
c) W.C.B of CD = 222015
1
d) W.C.B of DE = 3200301
N
IIV
BContd…
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COMPASS SURVEYING 193193
EW
S
Line AB is in first quadrant
In first quadrant the value of WCB = QB
QB values are always w.r.t to N & S
450301 N 450301E
QB of AB = N 45030
1E
IIIIIA
N
W.C.B of BC = 125045
1
Contd…
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COMPASS SURVEYING 194194
EW
S
Line BC is in second quadrant i.e. SE
QB = 1800 – W.C.B
= 1800
- 1250
451
= 540151
W.C.B of 1250451 = QB S540151E
I
IIIII
IV
B
C
N
W.C.B of CD = 222015
1
I QuadrantIV Quadrant
Contd…
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COMPASS SURVEYING 195195
EW
SLine CD is in third quadrant
If the line is in third quadrant
QB = W.C.B – 1800
= 222015
1 – 1800
= 410151
QB = S410151W
Q
II Quadrant
III Quadrant
IV Quadrant
C
D
N
W.C.B of DE = 320030
1
E
Contd…
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COMPASS SURVEYING 196196
EW
SLine DE is in fourth quadrant
W.C.B = 3200301
QB = 3600 – W.C.B
QB = 3600 - 320
030
1
= 390301
QB = N 390301 W
I Quadrant
II QuadrantIII Quadrant
IV Quadrant
D
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COMPASS SURVEYING 197197
8.Convert the following W.C.B to Quadrantal bearing
a) W.C.B of 450301
b) W.C.B of 1220301
c) W.C.B of 2250001
d) W.C.B of 3050301
N
IIV
BContd…
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COMPASS SURVEYING 198198
EW
S
ø = 450301 is in first quadrant
WCB = QB = N450301E
IIIIIA
N
W.C.B of 122030
1Contd…
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COMPASS SURVEYING 199199
EW
S
QB = 1800 – W.C.B = S E
= 1800 - 122030
1
= S770301E
QB = S770301E
I
IIIII
IV
B
C
N
W.C.B of 225000
1
I Q d t
Contd…
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COMPASS SURVEYING 200200
EW
S
I Quadrant
II Quadrant
III Quadrant
IV Quadrant
C
D
ø3 = 2250001 is in third quadrant
QB = W.C.B – 1800 = SW
= 2250001 – 1800 = S450001W
QB = S450001W
N
W.C.B of 305030
1
I Q d t
E
Contd…
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COMPASS SURVEYING 201201
EW
S
QB = 3600 – W.C.B = NW
QB = 3600 - 305
030
1
= N550301W
W.C.B of 305030
1 = QB of N 550301 W
I Quadrant
II QuadrantIII Quadrant
IV Quadrant
D
9. Convert the following whole circle bearings into reduced
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COMPASS SURVEYING 202202
bearings.
a) 46010
1
b) 226010
1
c) 1190201
d) 298040
1
IIV
NB
46010l
Contd…
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COMPASS SURVEYING 203203
46010l it is in first quadrant
W.C.B = Q.B
46010l = N 46010l E
IIIII
E
S
W A
IIV
NContd…
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COMPASS SURVEYING 204204
226010l is in third quadrant
Q.B = W.C.B – 1800 = SW
Q.B = 2260
10l
– 1800
Q.B = S 460101 W
IIIII
E
S
W A
B
226010l
IIV
N
119020l
Contd…
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COMPASS SURVEYING 205205
119020l is in second quadrant
Q.B = 1800 – W.C.B
Q.B = 1800 – 119020l
Q.B = S 600401 E
IIIII
E
S
W A
B
119020l
IIV
N
B
Contd…
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COMPASS SURVEYING 206206
298040l is in fourth quadrant
Q.B = 3600 – W.C.B 1800
Q.B = 3600 – 298040lQ.B = N 61020l W
IIIII
E
S
W A298040l
10. Convert the following whole circle bearing into reduced
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COMPASS SURVEYING 207207
g g
bearing.
a) 1690301
b) 3510101
c) 2800201
d) 990201
IIV
N
169030l
Contd…
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COMPASS SURVEYING 208208
169030l it is in second quadrant
Q.B = 1800 - W.C.B
Q.B = 1800 - 169030l
Q.B = S 10030l E
IIIII
E
S
W A
B
169 30
IIV
NBContd…
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COMPASS SURVEYING 209209
351010l is in fourth quadrant
Q.B = 3600 – W.C.B
Q.B = 3600 – 351010l
Q.B = N 80501 W
II
III
E
S
WA
351010l
IIV
N
B
Contd…
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COMPASS SURVEYING 210210
280020l is in fourth quadrant
Q.B = 3600 – W.C.B
Q.B = 3600 - 280020l
Q.B = N 790401 W
IIIII
E
S
W A
B
280020l
IIV
NContd…
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COMPASS SURVEYING 211211
99020l is in second quadrant
Q.B = 1800 – W.C.B
Q.B = 1800 – 99020l Q.B = S 80040l E
IIIII
E
S
W AB99
020l
11. Convert the following whole circle bearing into quadrantal
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COMPASS SURVEYING 212212
bearing.
a) 440301
b) 1240301
c) 181001
d) 2890301
IIV
N B
44030l
Contd…
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COMPASS SURVEYING 213213
44030l it is in first quadrant
W.C.B = Q.B
Q.B = N 44030l E
IIIII
E
S
W A
44 30
IIV
N
124030l
Contd…
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COMPASS SURVEYING 214214
124030l is in second quadrant
Q.B = 1800 – W.C.B
Q.B = 1800 – 124030l
Q.B = S 55030l E
IIIII
E
S
W A
B
124030l
IIV
NContd…
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COMPASS SURVEYING 215215
18100l is in third quadrant
Q.B = W.C.B – 1800
Q.B = 18100l - 1800
Q.B = S 1001 W
II
III
E
S
W A
B
18100l
IIV
NContd…
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COMPASS SURVEYING 216216
289030l is in fourth quadrant
Q.B = 3600 – W.C.B
Q.B = 3600 – 289030l
Q.B = N700301 W
II
III
E
S
WA
B 289030l
Problems
1.Convert the following Q.Bs into W.C.B.
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217/577
COMPASS SURVEYING 217217
1.Convert the following Q.Bs into W.C.B.
a) N450301W
b) N600401W
c) N30201W
d) S56001E
IIV
N
B
45030l
Contd…
-
8/19/2019 Buiding Services Compass Survey
218/577
COMPASS SURVEYING 218218
45030l is in fourth quadrant
Q.B = 3600 – W.C.B
Q.B = 3600 - 45030l
Q.B = N 314030lW
IIIII
E
S
W A
IIV
N
B
60040l
Contd…
-
8/19/2019 Buiding Services Compass Survey
219/577
COMPASS SURVEYING 219219
60040l is in fourth quadrant
W.C.B = 3600 – 60040l
Q.B = N 299020lW
IIIII
E
S
W A
IIV
NB
3020l
Contd…
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8/19/2019 Buiding Services Compass Survey
220/577
COMPASS SURVEYING 220220
The line is in fourth quadrant
Q.B = 3600 – W.C.B
Q.B = 3600 - 3020l
Q.B = N 356040lW
IIIII
E
S
W A
IIV
NContd…
-
8/19/2019 Buiding Services Compass Survey
221/577
COMPASS SURVEYING 221221
The line is in second quadrant
W.C.B = 1800 – Q.B
Q.B = 1800 – 5600lQ.B = S 12400l E
IIIII
E
S
W A
B
5600l
2.Convert the following Q.B into W.C.B.
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222/577
COMPASS SURVEYING 222222
a) S260141E
b) N780181W
c) N69091E
d) S320151W
IIV
NContd…
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8/19/2019 Buiding Services Compass Survey
223/577
COMPASS SURVEYING 223223
The line is in second quadrant
W.C.B = 1800 – Q.B
Q.B = 1800
– 260
14l
Q.B = S 153046l E
IIIII
E
S
W A
B
26014l
IIV
N
B
78018l
Contd…
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224/577
COMPASS SURVEYING 224224
78018l is in fourth quadrant
W.C.B = 3600 – Q.B
Q.B = 3600 - 78018l
Q.B = N 281042lW
IIIII
E
S
W A
IIV
NB
6909l
Contd…
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225/577
COMPASS SURVEYING 225225
6909l it is in first quadrant
W.C.B = Q.B
Q.B = N 6909l E
IIIII
E
S
W A
IIV
NContd…
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226/577
COMPASS SURVEYING 226226
32015l is in third quadrant
W.C.B = Q.B + 1800
Q.B = 320
15l
+ 1800
Q.B = S 2120151 W
IIIII
E
S
W A
B
32015l
3.Convert the following Q.B into W.C.B.
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227/577
COMPASS SURVEYING 227227
a) S460241W
b) S220181E
c) N82091W
d) N320221E
IIV
NContd…
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8/19/2019 Buiding Services Compass Survey
228/577
COMPASS SURVEYING 228228
46024l is in third quadrant
W.C.B = Q.B + 1800
Q.B = 460
24l
+ 1800
Q.B = S 2260241 W
IIIII
E
S
W A
B
46024l
IIV
NContd…
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229/577
COMPASS SURVEYING 229229
The line is in second quadrant
W.C.B = 1800 – Q.B
Q.B = 1800 – 22018l
Q.B = S 157042l E
IIIII
E
S
W A
B
22018l
IIV
N
B
8209l
Contd…
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230/577
COMPASS SURVEYING 230230
8209l is in fourth quadrant
W.C.B = 3600 – Q.B
Q.B = 3600 - 8209l
Q.B = N 277051lW
IIIII
E
S
W A
IIV
N B
32022l
Contd…
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231/577
COMPASS SURVEYING 231231
32022l it is in first quadrant
W.C.B = Q.B
Q.B = N 32022l E
IIIII
E
S
W A
4.Convert the following Q.B into W.C.B.
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232/577
COMPASS SURVEYING 232232
a) S370301E
b) S430151W
c) N73001W
d) N120451E
IIV
NContd…
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233/577
COMPASS SURVEYING 233233
The line is in second quadrant
W.C.B = 1800 – Q.B
W.C.B = 1800 – 37030lW.C.B = S 142030l E
IIIII
E
S
W A
B
37030l
IIV
NContd…
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234/577
COMPASS SURVEYING 234234
43015l is in third quadrant
W.C.B = Q.B + 1800
W.C.B = 430
15l
+ 1800
W.C.B = S 2230151 W
IIIII
E
S
W A
B
43015l
IIV
N
B
7300l
Contd…
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235/577
COMPASS SURVEYING 235235
8209l is in fourth quadrant
W.C.B = 3600 – Q.B
W.C.B = 3600 - 7300lW.C.B = N 28700lW
IIIII
E
S
W A
IIV
N B
12045l
Contd…
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236/577
COMPASS SURVEYING 236236
12045l it is in first quadrant
W.C.B = Q.B
W.C.B = N 12045l E
IIIII
E
S
W A
5.Convert the following Q.B into W.C.B.
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COMPASS SURVEYING 237237
a) N840301W
b) S38001E
c) S410301W
d) N15001W
IIV
N
B
84030l
Contd…
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238/577
COMPASS SURVEYING 238238
84030l is in fourth quadrant
W.C.B = 3600 – Q.B
W.C.B = 3600 - 84030lW.C.B = N 275030lW
IIIII
E
S
W A
IIV
NContd…
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239/577
COMPASS SURVEYING 239239
The line is in second quadrant
W.C.B = 1800 – Q.B
W.C.B = 1800 – 3800lW.C.B = S 14200l E
IIIII
E
S
W A
B
3800l
IIV
NContd…
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240/577
COMPASS SURVEYING 240240
41030l is in third quadrant
W.C.B = Q.B + 1800
W.C.B = 410
30l
+ 1800
W.C.B = S 2210301 W
IIIII
E
S
W A
B
41030l
IIV
N
B
1500l
Contd…
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241/577
COMPASS SURVEYING 241241
1500l is in fourth quadrant
W.C.B = 3600 – Q.B
W.C.B = 3600 - 1500lW.C.B = N 34500lW
IIIII
E
S
W A
6.Convert the following Q.B into W.C.B.
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242/577
COMPASS SURVEYING 242242
a) S150451W
b) N430451E
c) N210301E
d) S630301W
IIV
NContd…
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8/19/2019 Buiding Services Compass Survey
243/577
COMPASS SURVEYING 243243
15045l is in third quadrant
W.C.B = Q.B + 1800
W.C.B = 150
45l
+ 1800
W.C.B = S 1950451 W
IIIII
E
S
W A
B
15045l
IIV
N B
43045l
Contd…
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244/577
COMPASS SURVEYING 244244
43045l it is in first quadrant
W.C.B = Q.B
W.C.B = N 43045l E
IIIII
E
S
W A
IIV
N B
21030l
Contd…
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245/577
COMPASS SURVEYING 245245
21030l it is in first quadrant
W.C.B = Q.B
W.C.B = N 21030l E
IIIII
E
S
W A
IIV
N
A
Contd…
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246/577
COMPASS SURVEYING 246246
63030l is in third quadrant
W.C.B = Q.B + 1800
W.C.B = 63
0
30
l
+ 180
0
W.C.B = S 2430301 W
IIIII
E
S
W A
B
63030l
7.Convert the following Q.B into W.C.B.
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COMPASS SURVEYING 247247
a) N460101E
b) S460101W
c) S600
401
E
d) N610201W
IIV
N
EW
B
46010l
Contd…
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248/577
COMPASS SURVEYING 248248
46010l it is in first quadrant
W.C.B = Q.B
W.C.B = N 46010l E
IIIII
E
S
W A
IIV
N
EW A
Contd…
-
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249/577
COMPASS SURVEYING 249249
46010l is in third quadrant
W.C.B = Q.B + 1800
W.C.B = 46
0
10
l
+ 180
0
W.C.B = S 2260101 W
IIIII
E
S
W A
B
46010l
IIV
NContd…
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250/577
COMPASS SURVEYING 250250
The line is in second quadrant
W.C.B = 1800 – Q.B
W.C.B = 1800 – 60040lW.C.B = S 119020l E
IIIII
E
S
W A
B
60040l
IIV
N
EW
B
61020l
Contd…
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8/19/2019 Buiding Services Compass Survey
251/577
COMPASS SURVEYING 251251
61020l is in fourth quadrant
W.C.B = 3600 – Q.B
W.C.B = 3600 - 61020lW.C.B = N 298040lW
IIIII
E
S
W A
8.Convert the following Q.B into W.C.B.
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COMPASS SURVEYING 252252
a) N 470301 E
b) S 65001 E
c) S 410301 W
d) N 20001 W
IIV
N
EW
B
47030l
Contd…
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253/577
COMPASS SURVEYING 253253
47030l it is in first quadrant
W.C.B = Q.B
W.C.B = N 47030l E
IIIII
E
S
W A
IIV
NContd…
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254/577
COMPASS SURVEYING 254254
The line is in second quadrant
W.C.B = 1800 – Q.B
W.C.B = 1800 – 6500lW.C.B = S 11500l E
IIIII
E
S
W A
B
6500l
IIV
N
EW A
Contd…
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255/577
COMPASS SURVEYING 255255
41030l is in third quadrant
W.C.B = Q.B + 1800
W.C.B = 41030l + 1800
W.C.B = S 2210301 W
IIIII
E
S
W A
B
41030l
IIV
N
EW A
B
2000l
Contd…
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256/577
COMPASS SURVEYING 256256
2000l is in fourth quadrant
W.C.B = 3600 – Q.B
W.C.B = 3600 - 2000lW.C.B = N 34000lW
IIIII
E
S
W A
9.Convert the following QB into W.C.B
Contd…
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257/577
COMPASS SURVEYING 257257
a) QB of AB = S360301W
b) QB of BC = S430301E
c) QB of CD = N260451E
d) QB of DE = N400151W
N
I QuadrantIV Quadrant
Contd…
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COMPASS SURVEYING 258258
EW
S
II Quadrant
III Quadrant
A
B
Third quadrant S.W W.C.B = QB + 1800
= 360301 + 1800 = 2160301
W.C.B = 2160301
N
Q.B of BC = S430301E
IIV
Contd…
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COMPASS SURVEYING 259259
EW
IIIII
B
C
Second quadrant Q.B = S.E = W.C.B = 1800- 43030
1
W.C.B = 1360
301
S
N
IIV
D
Q.B of CD = N26045
1E
Contd…
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260/577
COMPASS SURVEYING 260260
EW
S
I
IIIII
IV
C
W.C.B = NE = WCB = QB
W.C.B = 260451
N
Q.B of N400151W
I QuadrantIV Quadrant
D
Contd…
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261/577
COMPASS SURVEYING 261261
EW
S
II QuadrantIII Quadrant
C
Angle is in Fourth quadrant
W.C.B = 3600-Q.B
= 3600 - 400151
W.C.B = 3190451
10.Convert the following QB into W.C.B
-
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262/577
COMPASS SURVEYING 262262
a) N400151E
b) S180141W
c) N240201Wd) S34031E
N
IIV
B
Contd…
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263/577
COMPASS SURVEYING 263263
EW
S
I
IIIII
IV
A
AB line is in First Quadrant
W.C.B = QB = 40
0
15
1
N
I QuadrantIV Quadrant
Contd…
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264/577
COMPASS SURVEYING 264264
EW
S
II Quadrant
III Quadrant
B
C
BC is in Third quadrant
W.C.B = QB + 1800
= 18014
1 + 1800
W.C.B = 1980141
N
N240201W
I QuadrantIV Quadrant
D
Contd…
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265/577
COMPASS SURVEYING 265265
EW
S
II QuadrantIII Quadrant
C
The DC is in Fourth quadrant
W.C.B = 3600-Q.B
= 3600 - 240201
W.C.B = 3350401
N
S34031E
IIV
Contd…
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8/19/2019 Buiding Services Compass Survey
266/577
COMPASS SURVEYING 2669C-105.40 266
EW
S
IIIII
D
E
The DE is in Second quadrant
W.C.B = 1800- Q.B
= 1800- 34031
W.C.B = 1450571
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267/577
Contd…
The bearing in the direction from A to B is Fore bearing of AB ,
say α
-
8/19/2019 Buiding Services Compass Survey
268/577
COMPASS SURVEYING 268
say α .
This is simply called bearing of AB
The bearing of line AB in the direction from B to A is Back
bearing of AB , say β
Contd…
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COMPASS SURVEYING 269
FIG.1
Referring to Fig 1
Let the fore bearing of a line AB = αо
Contd…
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8/19/2019 Buiding Services Compass Survey
270/577
COMPASS SURVEYING 270
Back bearing of BA= βo
(Or)
β = (1800 + ∟SBA)
= ∟BAN’
= α + 1800
Back bearing = Fore bearing + 1800 … (i)
Contd…
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271/577
COMPASS SURVEYING 271
Fig 2
Now , consider the bearing of BA as Fore bearing = β
Contd…
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8/19/2019 Buiding Services Compass Survey
272/577
COMPASS SURVEYING 272
Then , α = (1800 ~ ∟S’AB )
= (1800 ~ ∟ABN)
= 1800 ~ (3600 ~ β)
= ( β ~ 1800)
(or )
Back bearing = Fore bearing ~ 1800 … (ii)
Equations (i) and (ii) may be combined into one equation
i.e.
Contd…
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COMPASS SURVEYING 273
Back bearing = Fore bearing ± 1800
Use + ve sign if the Fore Bearing is less than 1800
Use – ve sign if the Fore Bearing is more than 1800
The rule is applicable for W.C.B System only
Contd…
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COMPASS SURVEYING 274
If Q.B’s are given , convert them into W.C.B’s
And apply the above rule and reconvert into Q.B’s
(or)
In case of Q.B’s the numerical value of FB’s and BB’s are
same.
But the cardinal directions are reversed as follows
Contd…
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COMPASS SURVEYING 275
For North, substitute South and vice-versa
For East, substitute West and vice-versa
The following example illustrates all the above cases
Example 1:
The following are the observed Fore bearings of some lines in a
traverse. Find their Back bearings.
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COMPASS SURVEYING 276
1) AB 420 30’
2) BC 1350
15’
3) CD 2120 30’
4) DE 2850 45’
Solution
1) F.B of AB = 420 30’
B B f AB (420 30’+1800)
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8/19/2019 Buiding Services Compass Survey
277/577
COMPASS SURVEYING 277
B.B of AB = (420 30’+1800)
= 2220 30’
2) F.B of BC = 1350 15’
B.B of AB = (1350 15’+1800 )
= 3150 15’
Contd…
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278/577
COMPASS SURVEYING 278
Fig.3A Fig.3B
3) F.B of CD = 2120 30’
. . B.B of CD = (2120 30’ ~ 1800)
Contd…
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279/577
COMPASS SURVEYING 279
... B.B of CD (212 30 180 )
= 320 30’
4) F.B of DE = 2850 45’
... B.B of DE = (2850 45’ ~ 1800)
=1050 15’
Contd…
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COMPASS SURVEYING 280
Fig.4A Fig.4B
Example :2
The F.B of AB is N 300 E .Find its B.B
-
8/19/2019 Buiding Services Compass Survey
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COMPASS SURVEYING 281
Solution:
The F.B of AB is N 300 E
The B.B of AB is S 300
W.
Solution by converting to WCB system
The F.B of AB is N 300 E
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COMPASS SURVEYING 282
The F.B of AB is in WCB = 300
The B.B of AB is in WCB = 300+1800
= 2100
By reconverting into Q.B The B.B of AB is S 300 W.
Calculation of included anglesCase 1:-
When the bearings of two line measured from same station
(From their point of inter section)
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COMPASS SURVEYING 283
( p ) Let F. B of AB is θ1 and AC is θ2 as shown below
Angle ∟BAC
= (Bearing of BC ~ Bearing of AB)
= (θ2 - θ1 )= (Bearing of preceding line ~ bearing of succeeding line)
A
B
C
N
θ2θ1
Fig.5
Case:2
When the bearings of two lines measured from different
stations
Contd…
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COMPASS SURVEYING 284
A
B
θ1
θ2
C
Fig.6
In this case express the bearings of two
– Lines as if measured from single station
– And apply the formula
Contd…
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COMPASS SURVEYING 285
pp y
Thus find B.B of AB
Then ∟B = F.B of BC ~ B.B of AB
Note:-
1) When two lines meet at a point two angles
– The interior and exterior angles are formed
– The sum of these angles = 3600
Contd…
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COMPASS SURVEYING 286
g
– ... If the calculated interior angle is >1800 it is exterior
– The interior angle then is = 3600 ~ exterior angle.
2) If the bearing are given in Q.B . System convert them to
W.C.B system and then apply the above rules
– The following numerical examples illustrates the above
cases.
Contd…
Note :-
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COMPASS SURVEYING 287
“ ~ ”This symbol indicates difference.
Therefore whether we subtract bigger bearing from smaller
bearing
or
vice-versa
we should take only numerical value into consideration
Example 3
Find the angle between the lines OA &OB given their bearings as
below
350 30’ d 1500 45’
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COMPASS SURVEYING 288
350 30’ and 1500 45’
Solution :
Draw the sketch.
From sketch ∟AOB = Bearing of OB ~ bearing of OA
= 1500 45’ ~ 350 30`
= 1150 15’
Contd…
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COMPASS SURVEYING 289
Fig.7
Example 4
Find the angle between the lines OA &OB given their bearings as
below
200 15’ and 3230 30’
Solution :
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290/577
COMPASS SURVEYING 290
Draw the sketch.
From sketch ∟AOB = bearing of OB ~ bearing of OA
= 3230 30’ ~ 200 15’
= 3030 15’>1800
= Indicates exterior angle
= 560
45’Therefore interior ∟AOB = 3600 ~ 3030 15
Contd…
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291/577
COMPASS SURVEYING 291
Fig.8
Example 5
Find the angle between the lines OA &OB given their bearings as
below
-
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COMPASS SURVEYING 292
1150 15’ and 2500 45’
Solution :
Draw the sketch.
From sketch ∟AOB = Bearing of OB ~ bearing of OA
= 2500 45’ ~ 1150 15’
= 1350 30’
Contd…
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293/577
COMPASS SURVEYING 293
Fig.9
Example 6
The bearings of AB and BC are given below. Find the angle
between the lines
1520 15’ and 700 30’
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COMPASS SURVEYING 294
Solution :
In this problem the bearings of lines are not from point of
intersection
Therefore express the bearings as if measured from point of
intersection
Then apply the rule.
Contd…
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COMPASS SURVEYING 295
Fig.10
Bearing of AB = 1520 15`
Bearing of BA = 1520 15` + 1800
= 3320 15`
Contd…
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296/577
COMPASS SURVEYING 296
(Note that Bearing of BA is nothing but B.B of AB)
Bearing of BC = 700 30’
Included ∟B = 3320 15 ~ 700 30’
= 2610 45’ > 1800 Indicates exterior angle.
Therefore Included ∟B = 3600 ~ 2610 45
= 980 15’
Example 7
The bearings of AB and BC are given below. Find the angle
between the lines
650 30’ and1150 15`
Solution :
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COMPASS SURVEYING 297
Bearing of AB = 650 30’
Bearing of BA = 650 30’+1800
= 2450 30’
(Note that Bearing of BA is nothing but B.B of AB)
Bearing of BC = 1150 15’
Included ∟B = 2450 30’ ~ 1150 15’
= 1300 15`
Contd…
-
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298/577
COMPASS SURVEYING 298
Fig.11
Example - 8
Find the include angle B given the following bearings
Bearing of AB, N 150 15` E and bearing of AC, N. 870 10` E
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COMPASS SURVEYING 299
Solution
Step(1)
Convert the given Q. Bs into W. C. Bs
Step(2)
Apply the formula as usual
W.C.B of AB = 15015`
W.C.B of AC = 870
10`
Contd…
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∟BAC = (W.C.B of AC ~ W.C.B of AB)
= 87010` ~ 15015`
= 71055`
Find the include angle B given the following bearings:
Bearing of AB, N 120 24` E and bearing of AC, S. 520 30` E
Contd…
Example - 8
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g , g ,
Solution
Step(1):
Convert the given Q. Bs into W. C. Bs
Step(2):
Apply the formula as usual
W.C.B of AB = 12024`
W.C.B of AC = 1800 ~ 52030`
Contd…
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= 127030`
∟BAC = (W.C.B of AC
~ W.C.B of AB)
= 12024` ~ 127030`
= 11506`
Example - 9
The bearing of line AB is N.620 45` E ;
CA is N.280 15`E Find angle BAC
Solution
C t th b b i i t W C B' d l th l
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Convert the above bearings into W.C.B's and apply the rule
W.C.B if AB = 620 45`
Bearing of CA = N.280 15`W
Bearing of AC = S 280 15`WW.C.B of AC = 280 15` + 1800
= 2080 15`
angle BAC = Bearing of AB ~ Bearing of AC
= 620 45` ~ 2080 15`
= 1450 30`
From the above two examples ,we can conclude that
In a traverse angle between two successive lines
Contd…
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In a traverse angle between two successive lines
= (Back bearing of preceding line ~ bearing of succeeding line)
Procedure to calculate included angles of a Traverse
Draw the required sketch
Carefully enter the readings
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If only fore bearings are given, find corresponding back
bearings.
If the bearings are given in Q. Bs, convert them into W. C. Bs
and find the included angles
Apply the check that the sum of interior angles
Contd…
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= (2n-4) x 900
Where ‘n’ is the no. of sides of the traverse
Example - 1
The following bearings were taken in a closed traverse
ABCD
Line Fore bearing Back bearing
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Calculate the interior angles of the traverse
Line Fore bearing Back bearing
AB 45015` 2250 15`
BC 1230 15` 3030 15`
CD 1810 00` 10 00`
DA 2890 30` 1090 30`
Solution :
Calculation of the interior angles of the closed traverse ABCD
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Fig.1
Contd..
A = (Fore bearing of AB – Back Bearing of DA)
= (450 15` -1090 30`)
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( )
= 640 15`
B = (Fore Bearing of BC – Back Bearing of AB)
= (1230 15 - 2250 15`0 )
= 1020 00`
Contd…
Check : ∟A + ∟B+ ∟C+ ∟D
= 640 15` + 1020 00`+ 1220 15`+ 71030`
= 3600 O.K
A= 640 15`
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A= 640 15
B= 1020 00`
C=1220 15`
D=710
30`
Contd…
The arrow marks indicated below in the table may be followed
for calculation of included angles
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Line Fore bearing Back
bearing
AB 45015` 2250 15`
BC 1230 15` 3030 15`
CD 1810 00` 10 00`
DA 2890 30` 1090 30`
Example - 2 The bearing of the sides of a closed transverse ABCDEA are as
follows
Side F.B B.B
AB 1070 15` 2870 15`
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Compute the interior angles of the traverse and exercise necessary
checks
AB 1070 15 2870 15
BC 220 00` 2020 00`
CD 2810 30` 1010 30`
DE 1810 15` 10 15`
EA 1240 45` 3040 45`
Contd…
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Fig.2
Solution
(i) The included ∟A = (FB of AB ~ BB of EA )
= (1070 15` ~ 3040 45`)
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= (1070 15 ~ 3040 45 )
= 197030` > 1800 (Exterior)
= 3600 ~ 197030` = 162030`
Contd..
(ii) Included angle at B:
= ( FB of BC ~ BB of AB)
= (220 00` ~ 2870 15`)= (2650 15`>1800 ) (Exterior)
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= (2650 15 >1800 ) (Exterior)
= (3600 ~ 265015`)
= 940 45`
(iii) Included angle at C:
= (FB of CD ~ BB of BC)
= (2810
30` ~ 2020
00`)= 790 30`
(iv) Included angle D
= (FB of DE ~ BB of CD)
= (1810 15` ~ 1010 30`)
Contd..
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= 790 45`
(v) Included angle E
= (FB of EA ~ BB of DE)
= (1240 45` ~ 10 15)
= 1230 30`
Check
Sum of the included angles of a pentagon
= (2x